Multi-wavelength polarimetric observations of blazars reveal complex energy-dependent polarization behavior,
with a decrease in polarization fraction from X-ray to millimeter bands and significant variability in the electric
vector position angle (EVPA). These trends challenge simple, single-zone synchrotron models and suggest a more intricate,
turbulent jet structure with multiple emission zones.
This work aims to develop a statistical framework to model the energy-dependent polarization patterns observed in blazars,
particularly focusing on the behavior captured by IXPE in the X-ray and RoboPol in the optical. The goal is to determine
the statistical characterization of multi-zone model, in terms of the cell size distribution, and of the distribution
of the physical parameters of the electron energy distribution (EED).
A Monte Carlo simulation approach was employed to generate synthetic multi-zone synchrotron emission, using the
JetSeT code, from a spherical region populated by turbulent cells with randomly distributed physical properties.
Simulations were run across various scenarios: from identical cells to power-law distributed cell sizes and EEDs with
different cut-off and low-energy slope distributions. Simulation results were compared to observed IXPE and RoboPol polarization trends.
Our analysis demonstrates that the observed energy-dependent polarization patterns can be explained by a purely turbulent,
multi-zone model without requiring a correlation between the cell size and the EED parameters. The key determinant of
polarization is the effective number (flux-weighted) of emitting cells, which is significantly modulated by the dispersion
in cell properties, especially the EED cut-off energy, at higher frequencies, and the dispersion in the EED low-energy
spectral index, at lower frequencies.
Using a fractional dispersion on the EED cutoff of the order of 90\%, and a dispersion of the EED
low-energy spectral index between $\approx 0.5$ and $\approx 1.5$, our model reproduces both the mm-to-X-ray polarization
trends, observed in IXPE multiwavelength campaigns, and the optical polarization dependence on synchrotron peak frequency,
observed in the RoboPol dataset.